Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set: 14

Answer

$(y+1)(y+7)$

Work Step by Step

The 2 numbers whose product is $ac= 1(7)=7 $ and whose sum is $b= 8 $ are $\left\{ 1,7 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ y^2+8y+7 ,$ then \begin{array}{l}\require{cancel} y^2+1y+7y+7 \\\\= (y^2+y)+(7y+7) \\\\= y(y+1)+7(y+1) \\\\= (y+1)(y+7) .\end{array}
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